Re: Infinity

thinkdesigns - isn't that why it's so interresting?

Jimmymcjummingtin - You have to imagine a set

where the three dots represent an infinite amount of the preceding number. This gives you an infinite amount of 1's, followed by an infinite amount of 2's and then an infinite amount of 3's and so on. Ricky's claim is then that the set would only include 1's, since the proceding numbers wouldnt be included(you can't reach an infinite amount of 1's, which you would need to move on to filling in 2's). Dunno if it helps(or if it's correct? )

Re: Infinity

100% correct Patrick. Think of it this way. At what position in the set would there be a 2?

to me it seems mroe symbolic than mathematical, and ironically, if something is infinite, then it is beyond our understanding anyway, and so there is no point ever trying to consider what it is like because we will always fall short

When you get up to higher maths, you find that all of math is symbolic.

Infinity is not beyond our understanding. It is beyond many peoples understanding, that is true. But not a mathematicians. For example:

f(x) = 1/x

We know what would happen if we reach infinity. f(x) = 0. Of course, we never do reach infinity, but we know what would happen if we did.

Mathematicians have been studying infinity for hundreds of years. And we know a heck of a lot about it. We know it has properties, just like anything else in math. We know that if we come across it in equations, we can use tricks to get rid of it.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."